Question

7. The test scores of one hundred students reveal a mean of 70 and a standard deviation of 5. According to Chebyshev:

1. what % of students will score between 60% and 80%?
2. what % of students will score between 63% and 77%?

**Please show work

Answer 1

7. a) Chebyshev theorem states that the proportion of the distribution within "k" standard deviation of the mean is at-least 1 - (1/k2)

Now, we need to find out the proportion of students that will score between 60 and 80,

60 = u - s*k = 70 - 5*k

80 = u + s*k = 70 + 5*k

k = 2

Proportion of students = 1 - (1/4) = 3/4 = 0.75

Hence, atleast 75% of the students will score between 60 and 80.

b) We need to find out the proportion of students that will score between 63 and 77,

63 = u - s*k = 70 - 5*k

77 = u + s*k = 70 + 5*k

k = 1.40

Proportion of students = 1 - (1/1.96) = 0.49

Hence, atleast 49% of the students will score between 63 and 77.